Max Normal Stress of Beam: 1.879N | Modulus of Elasticity 100Gp

[pirateman99]

Homework Statement

What is the maximum normal stress in the beam and where is it located? The beam is 1m long, 0.2m high, and 0.05m thick (out of the page). The Modulus of Elasticity is 100Gp. The force is applied at an angle of 20 degrees with horizontal.

|
|____________
| |- - - - -- - (Imaginary horizontal)
|____________| -- 20deg
| --
--
F= 2N

(the picture is kind of messed up but just imagine a force being applied 20 degrees downward of the horizontal out of the end of the beam, so pretty much straight out of the end of the beam but at a slight angle.

The Attempt at a Solution

I calculated that it is 1.879N in x direction and .684N in y direction and that sigx is 187.7 N/m^2

Everywhere I see makes it look like i use equation My/I but I do not know how to calculated y or I and I do not know how any of that plays into this.

Any help would be awesome

Thanks.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

The Attempt at a Solution

I calculated that it is 1.879N in x direction and .684N in y direction and that sigx is 187.7 N/m^2

Good so you have the components of the force. One produces a normal stress which you've found. The vertical component produces a bending stress.

Everywhere I see makes it look like i use equation My/I but I do not know how to calculated y or I and I do not know how any of that plays into this.

Any help would be awesome

Thanks.

You said the dimensions of the beam are 1 m long, 0.2 m high and 0.05 m wide, so if you look at the beam from the front, the dimensions are just 0.2 m x 0.05 m. So what shape does that form? (You can look up I for that section).

'y' is just the distance from the neutral axis. Since the shape is a simple shape, the neutral axis coincides with the centroidal axis. So the maximum value for 'y' would be from the neutral axis to the furthest point. (What distance is this?)

I think you should know how to calculate M, the bending moment.

 

[pongo38]

rock.freak667: Perhaps what you need to know, and it's not obvious is that normal stresses arise from both normal forces, and from bending moments. So you need a combined normal stress equation.

 

[rock.freak667]

rock.freak667: Perhaps what you need to know, and it's not obvious is that normal stresses arise from both normal forces, and from bending moments. So you need a combined normal stress equation.

Yes, but I did not tell the OP how to combine it, I assumed they'd have the formula to do so since they have the formula for bending.

 

[DeeNos]

I would approach this problem by first understanding the given information and the variables involved. The maximum normal stress of the beam is 1.879N and the modulus of elasticity is 100Gp. The beam is 1m long, 0.2m high, and 0.05m thick and the force is applied at a 20 degree angle with the horizontal.

To find the location of the maximum normal stress, we need to understand the concept of bending stress in beams. Bending stress is the stress induced in a beam due to the applied load causing the beam to bend. The maximum bending stress occurs at the point farthest from the neutral axis of the beam, which in this case is at the top or bottom of the beam.

To calculate the maximum normal stress, we can use the formula for bending stress in a rectangular beam:

σmax = My/I

Where σmax is the maximum normal stress, M is the moment of the applied force, y is the distance from the neutral axis to the point of interest, and I is the moment of inertia of the cross-sectional area of the beam.

To find the moment of the applied force, we can use the formula:

M = F * d * cosθ

Where F is the applied force, d is the distance from the point of application to the neutral axis, and θ is the angle between the applied force and the horizontal.

In this case, F = 2N, d = 0.2m, and θ = 20 degrees. Plugging these values into the formula, we get M = 0.4N*m.

Next, we need to calculate the moment of inertia of the cross-sectional area of the beam. For a rectangular beam, the moment of inertia can be calculated using the formula:

I = (1/12) * b * h^3

Where b is the width of the beam and h is the height of the beam.

In this case, b = 0.05m and h = 0.2m. Plugging these values into the formula, we get I = 4.1667 * 10^-6 m^4.

Now, we can plug all of these values into the formula for maximum bending stress:

σmax = (0.4 N*m) * (0.2m) / (4.1667 * 10^-6 m^4)

= 1.